How would I make a cloudy backdrop in cycles?
Depending on what you want, your best option may be to just make a procedural sky.  Here is a great tutorial for that: https://www.youtube.com/watch?v=Tr6wTyfAO04  Making the clouds procedural will save you a ton on render times.  Although, if you are trying to fly through the clouds, they would need to be more volumetric and realistic.  Here is a great tutorial by BlenderGuru just for that: https://www.youtube.com/watch?v=TJ_OcBh7F5I

To make a simple cloud all you really need to do is connect a Volume Scatter node to your materials volume input.  



You can raise the density for a more stormy look.